epidemic modeling teams

Abstract: Challenges and chances of mathematical software are directly entangled with the programming language used. Depending on the background of developers and users, conflicts between different goals may arise. While several, e.g., scripting languages allow a low barrier and user-friendly entry to mathematical modeling and simulation, corresponding implementations will most likely not allow timely outcomes for detailed simulations. In infectious disease modeling, while several large-scale software frameworks rely on C or C++ implementations, most models are implemented in Python or R. While the latter allow for fast prototyping and more interactive development, it has been shown for several applications that C or C++ implementations outperform plain Python or R implementations by factors between one and three orders of magnitude. In particular, in times of pandemics, the urgent need for swift estimation of the system's dynamics makes the use of large-scale models in these noncompiled languages prohibitive. In order to create synergies and close the gap between scientists from the application and the computational domain, binding libraries allow to execute entire, compiled software frameworks from languages such as Python. However, with iterative model development, extension, or addition of new models, implementing bindings can represent another relevant barrier to developers of the C or C++ backends. In this paper, we show how a large-scale software framework with a multitude of infectious disease models can be efficiently exposed to Python. In addition, we suggest a semi-automated way to generate interface code by analyzing generic C++ code through abstract syntax trees, enabling a modularized approach working with intermediate representations.

Abstract: Computing diffusion processes on networks is fundamental to applications including influence maximization, epidemic modeling, information propagation, and diffusion inference. The Independent Cascade (IC) model is one of the most widely used models of progressive diffusion, yet exact computation of its activation probabilities is #P-hard, while Monte Carlo simulation becomes costly when accurate estimates are required repeatedly. Despite its central role, analytical approximation of the IC diffusion function has received comparatively little systematic attention relative to the extensive literature on influence-maximization algorithms. We present a comprehensive study of analytical approximations for the IC model. We review a wide range of existing approaches and unify them through a common framework based on temporal representation, retained propagation information, and aggregation rule. This perspective exposes connections between previously distinct approximation families and motivates several new methods. We further conduct, to our knowledge, the first large-scale cross-family comparison of analytical IC approximations for node-level marginal activation probabilities. Our benchmark spans real-world and synthetic networks with systematically varied topology, seed-set size, edge-probability model, and diffusion strength. The proposed second-order dynamic message-passing method achieves the lowest pooled median error and the lowest dataset- or graph-family-level median error on every network considered. The results reveal systematic differences between approximation families, identify regimes in which higher-order corrections are most beneficial, and establish analytical IC approximation as a rich accuracy-efficiency design space rather than a collection of isolated methods.

Abstract: Compartment models of infectious diseases are often linear in coefficients that are physical parameters or products or ratios of them. We exploit this with closed-form least squares and equip the estimates with distribution-free uncertainty. Physics-informed regression (PIR) fits the parameters to finite-difference derivatives of the data; we introduce physics-informed weak regression (PIWR), which integrates the model in time instead, needs no derivatives of the data, estimates the initial state jointly and is high-order accurate. To quantify uncertainty we wrap both estimators in split conformal prediction, with a calibration population generated by the physics-based model itself, giving simultaneous intervals for all parameters with a finite-sample coverage guarantee. A residual-adaptive factor, computed without ground truth, scales the intervals to each data set (PIWR-RACC). On the eleven benchmark models of disease-informed neural networks (DINNs), PIWR or PIR-FD6 is one to four orders of magnitude more accurate than the reported DINN results wherever the sampling resolves the dynamics, in about a millisecond per fit instead of minutes to hours of training, and the 90% intervals achieve 87-92% coverage in all 88 settings. On the S3I3R model of the original PIR study, PIWR lowers the reported PIR errors by about three orders of magnitude. On real data from the 1978 boarding-school influenza outbreak, a variable-projection variant gives calibrated 95% intervals that overlap those of a Bayesian analysis. On a time-varying transmission benchmark, a B-spline expansion of beta(t) keeps PIR and PIWR linear; they are more accurate than physics-informed neural networks in three of four cases and comparable in the noisiest, with simultaneous bands for beta(t). The complete conformal calibration takes less than two minutes for every benchmark.

Abstract: Comparing temporal networks is a challenging problem in network analysis. Commonly adopted methods compare structural properties of temporal graphs and can be highly sensitive to the pre-selected features. However, temporal networks are the support of dynamical processes, and a process may take place in statistically indistinguishable ways on structurally different temporal graphs. In particular, a dissimilarity measure that compares temporal graphs based on how spreading processes unfold on them is highly desirable. In this work, we first define the Time-Shift DTW, a dissimilarity between epidemic curves that accounts for both differences in their shape and temporal shifts. We then introduce Epidemic-Aware Temporal Graph Dissimilarity (EATGD), a deterministic and differentiable dissimilarity between temporal graphs that combines an embedding-based temporal graph distance with a set of topological and temporal features. Its parameters are calibrated using stochastic SIR simulations to maximize the correlation with the Time-Shift DTW, after which graph comparisons require no further epidemic simulations. Using empirical human proximity networks from the SocioPatterns collaboration and synthetic temporal graphs, we show that EATGD captures epidemic-based graph dissimilarity and generalizes across heterogeneous network settings. Its differentiability and computational efficiency make EATGD suitable for integration into machine-learning pipelines and provide a potential loss function for training generative models to reproduce epidemic dynamics without requiring an exact reconstruction of fine-grained network structure.

Abstract: Neural operators learn maps between function spaces, while hereditary network dynamics are described by Volterra resolvents with non-rational Laplace symbols. We introduce a fractional Laplace neural operator (fLNO) that embeds this structure in the learned map. For commuting excitation--Laplacian pairs, one block graph-spectral layer represents the full linear Volterra solution operator exactly. We establish an expressivity frontier for finite rational realizations: they approximate fractional memory geometrically on compact frequency windows, but cannot reproduce the non-integer critical asymptotics generated by a branch point, and on the half-line the best rational rate is root-exponential. The same theory yields trainable parametrizations that enforce a prescribed stability margin by construction, and a graphon-transfer theorem separates genuine operator consistency from parameter sharing. In a common-data benchmark, positive rational operators can match or exceed fLNO accuracy on finite horizons, whereas in controlled near-critical experiments fLNO recovers the branching coordinate more faithfully with far fewer parameters; unconstrained rational fits can cross the stability boundary, while certified parametrizations cannot. A four-parameter spectral law transfers without retraining from graphs of size 48 to 192 with 0.51--0.62% relative error. Applications to Chilean aftershock sequences and to renewal models for Chile and 21 Italian regions illustrate structured inference with explicit uncertainty. The contribution is an operator-learning architecture in which exact memory structure, physical coordinates and stability guarantees coexist with competitive accuracy.